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4MA1/2H Jun 2020, Question 10: Drawing Cumulative Frequency Diagrams

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2H (Higher) · Calculator · 7 marks

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The question, in short

From a grouped frequency table of 120 buses and their lateness in minutes, complete a cumulative frequency table, draw the cumulative frequency graph, then use it to estimate the interquartile range and the count of buses over 48 minutes late.

Summarised in our own words. Use the official paper for the exact wording and the diagram.

Part (a) · 1 mark

Fill in the cumulative frequency column for each upper class boundary from 10 up to 60, using the given frequencies.

  1. 1Cumulative frequency adds each frequency to the total so far.
  2. 20 < L ≤ 10: 10
  3. 30 < L ≤ 20: 10 + 16 = 26
  4. 40 < L ≤ 30: 26 + 44 = 70
  5. 50 < L ≤ 40: 70 + 29 = 99
  6. 60 < L ≤ 50: 99 + 15 = 114
  7. 70 < L ≤ 60: 114 + 6 = 120

Answer10, 26, 70, 99, 114, 120

Part (b) · 2 marks

Plot the cumulative frequency against the number of minutes late on the grid and draw the cumulative frequency curve.

  1. 1Plot points at (10,10), (20,26), (30,70), (40,99), (50,114), (60,120).
  2. 2Join points with smooth curve or straight line segments.

AnswerA cumulative frequency graph through (10, 10), (20, 26), (30, 70), (40, 99), (50, 114) and (60, 120)

Part (c) · 2 marks

Read lower and upper quartiles from your graph and subtract to estimate the interquartile range.

  1. 1Find lower quartile: 1/4 of 120 = 30
  2. 2Find upper quartile: 3/4 of 120 = 90
  3. 3Read off values from graph at cumulative frequencies 30 and 90.
  4. 4LQ ≈ 21, UQ ≈ 37
  5. 5Interquartile range = 37 − 21 = 16

Answer16 (accept 14 to 18)

Part (d) · 2 marks

Use your graph to estimate how many buses were more than 48 minutes late.

  1. 1Find cumulative frequency at 48 minutes.
  2. 2Reading from graph: at L = 48, cumulative frequency ≈ 111
  3. 3Number of buses more than 48 minutes late = 120 − 111 = 9

Answer9 (accept 7 to 10)

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